I am legally responsible if my ex-wife defaults on the mortgage if she was awarded the house by the court

Yes. Your mortgage obligation was a contract which you, your wife and your lender entered into. Your divorce agreement is a contract only between you and your wife, which the court adopts in its divorce decree. However, the lender is not a party to that agreement or to the divorce action, therefore its rights cannot be affected by what agreements the two of you make or by the divorce decree.

This is a situation that often "bites" people. Furthermore, if your wife lacks sufficient credit or income within the next 5 years to obtain a loan, even if she tries in good faith to do so, she will not be able to refinance and it would be difficult under those facts for the court to even hold her in contempt if she takes reasonable measures to try.